A simple group generated by involutions interchanging residue classes of the integers

Abstract

We present a countable simple group which arises in a natural way from the arithmetical structure of the ring of integers.

Simple groups generated by involutions interchanging residue classes modulo lattices in ℤd

“…In this paper we generalize the construction of the simple group CT.Z/ < Sym.Z/ investigated in [1] The work which led to the discovery of the simple group CT.Z/ was originally motivated by Lothar Collatz' 3n C 1 conjecture, which dates back to the 1930's. This conjecture asserts that iterated application of the so-called Collatz mapping…”

“…Simple groups generated by involutions interchanging residue classes 85 There is a straightforward generalization of Definition 3.6 and Corollary 3.7 in [1]: Definition 3.5. Given a set P of odd primes, let CT P .Z d / 6 CT.Z d / denote the subgroup which is generated by all class transpositions whose prime sets are subsets of P [ ¹2º.…”